Exploring Rational Exponents and Exponential Equations

What does a rational exponent represent in terms of roots?

• The base raised to the power of the root

• The root of the base raised to a power

• A multiplication of the base by the root

• A division of the base by the root

If an expression is written as 'b to the one-half power', what does it signify?

• b squared

• Square root of b

• b divided by 2

• b multiplied by 0.5

How would you express the cube root of a variable x using a rational exponent?

• x to the three

• x to the one-third power

• x to the three halves power

• x cubed

What is the result of 64 to the one-third power?

• 4

• 8

• 16

• 32

How is the fourth root of 81 expressed using a rational exponent?

• 81 to the fourth power

• 81 to the one-half power

• 81 to the four

• 81 to the one-fourth power

What does raising a number to the three-halves power involve?

• Cubing the number then taking the square root

• Taking the square root then cubing the number

• Tripling the number then halving it

• Halving the number then tripling it

If you have an equation 2 to the x equals 8, how can you solve for x?

• Subtract 2 from 8 and solve for x

• Divide 8 by 2 and set x to the result

• Multiply 2 by 8 and solve for x

• Rewrite 8 as 2 to the third and set x to 3

What is the value of x when 3 to the x plus 1 equals 27?

• x equals 5

• x equals 4

• x equals 3

• x equals 2

How do you solve 4 to the x minus 3 equals 64?

• Multiply 4 by 3, solve for x

• Divide 64 by 4, solve for x

• Set x minus 3 equal to 64, solve for x

• Set x minus 3 equal to 3, solve for x

What is the correct way to solve for x in the equation 5 to the 2x equals 25?

• Rewrite 25 as 5 squared, set 2x to 2

• Rewrite 25 as 5 to the third, set 2x to 3

• Multiply 5 by 5, set 2x to 25

• Divide 25 by 5, set 2x to 5